Noncommutative standard model: Difference between revisions

Revision as of 06:30, 22 December 2020

Revision as of 20:56, 24 December 2020

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==History==

First ideas to use [[noncommutative geometry]] to particle physics appeared in 1988-89

,<ref name="connes_1998_essay">

{{cite book

| last = Connes | first = Alain | author-link = Alain Connes

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| publisher=Oxford University Press

| ___location=New York

}}</ref><ref name="dv_1988_dcdnc">

<ref name="dv_1988_dcdnc">

{{cite journal | title = Dérivations et calcul différentiel non commutatif

| last = Dubois-Violette | first = Michel

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| year = 1988

}}

</ref><ref name="DVKM_1989_CBNG">

</ref>

<ref name="DVKM_1989_CBNG">

{{cite journal | title = Classical bosons in a non-commutative geometry

| last1 = Dubois-Violette | first1 = Michel

Line 105 ⟶ 103:

| year = 1989

| page = 1709 | doi = 10.1088/0264-9381/6/11/023 | bibcode = 1989CQGra...6.1709D }}

</ref><ref name="10.1016/0370-2693(89)90083-X">

</ref>

<ref name="10.1016/0370-2693(89)90083-X">

{{cite journal | title = Gauge bosons in a noncommutative geometry

| last1 = Dubois-Violette | first1 = Michel

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| doi = 10.1016/0370-2693(89)90083-X

| bibcode = 1989PhLB..217..485D }}

</ref><ref name="10.1063/1.528917">

</ref>

<ref name="10.1063/1.528917">

{{cite journal | title = Noncommutative differential geometry and new models of gauge theory

| last1 = Dubois-Violette | first1 = Michel

Line 131 ⟶ 127:

| doi = 10.1063/1.528917

}}

,</ref> and were formalized a couple of years later by [[Alain Connes]] and [[John_Lott_(mathematician)|John Lott]] in what is known as the Connes-Lott model

</ref>

.<ref name="10.1016/0920-5632(91)90120-4">

, and were formalized a couple of years later by [[Alain Connes]] and [[John_Lott_(mathematician)|John Lott]] in what is known as the Connes-Lott model

<ref name="10.1016/0920-5632(91)90120-4">

{{cite journal | title = Particle models and noncommutative geometry

| last1 = Connes | first1 = Alain

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| volume = 18 | issue = 2 | pages = 29–47 | doi = 10.1016/0920-5632(91)90120-4

| bibcode = 1991NuPhS..18...29C | hdl = 2027.42/29524 | hdl-access = free}}

.</ref> The Connes-Lott model did not incorporate the gravitational field.

</ref>

. The Connes-Lott model did not incorporate the gravitational field.

In 1997, [[Ali Chamseddine]] and [[Alain Connes]] published a new action principle, the Spectral Action

,<ref name="10.1007/s002200050126">

{{cite journal | title = The Spectral Action Principle

| last1 = Chamseddine | first1 = Ali H.

Line 159 ⟶ 153:

| arxiv = hep-th/9606001

| bibcode = 1997CMaPh.186..731C | s2cid = 12292414 }}

</ref>, that made possible to incorporate the gravitational field into the model. Nevertheless, it was quickly noted that the model suffered from the notorious fermion-doubling problem (quadrupling of the fermions)

<ref name="10.1103/PhysRevD.55.6357">

{{cite journal | title = Fermion Hilbert Space and Fermion Doubling in the Noncommutative Geometry Approach to Gauge Theories

Line 200 ⟶ 194:

| bibcode = 2007JMP....48a2303B | s2cid = 11511575 }}

</ref> and [[Alain Connes]]

,<ref name="10.1088/1126-6708/2006/11/081">

{{cite journal | title = Noncommutative Geometry and the standard model with neutrino mixing

| last = Connes | first = Alain

Line 210 ⟶ 204:

| arxiv = hep-th/0608226

| bibcode = 2006JHEP...11..081C | s2cid = 14419757 }}

,</ref> almost at the same time.

</ref>

, almost at the same time.

They show that massive neutrinos can be incorporated into the model by disentangling the KO-dimension (which is defined modulo 8) from the metric dimension (which is zero) for the finite space. By setting the KO-dimension to be 6, not only massive neutrinos were possible, but the see-saw mechanism was imposed by the formalism and the fermion doubling problem was also addressed.

Line 250 ⟶ 243:

<ref name="10.1007/JHEP09(2012)104"/> by taking into account a real scalar field that was already present in the model but was neglected in previous analysis.

Another solution to the Higgs mass problem was put forward by Christopher Estrada and [[Matilde Marcolli]] by studying renormalization group flow in presence of gravitational correction terms

.<ref name="10.1142/S0219887813500369">

{{cite journal | title = Asymptotic safety, hypergeometric functions, and the Higgs mass in spectral action models

| last1 = Estrada | first1 =Christopher

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| arxiv = 1208.5023

| bibcode = 2013IJGMM..1050036E | s2cid = 215930 }}

</ref>.

==See also==